Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915621883609088 |
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| author | Gaudio, Tiziano |
| author_facet | Gaudio, Tiziano |
| contents | We prove that all nice holomorphic vertex operator superalgebras (VOSAs) with central charge at most 24 and with non-trivial odd part are unitary, apart from the hypothetical ones arising as fake copies of the shorter moonshine VOSA or of the latter tensorized with a real free fermion VOSA. Furthermore, excluding the ones with central charge 24 of glueing type III and with no real free fermion, we show that they are all strongly graded-local. In particular, they naturally give rise to holomorphic graded-local conformal nets. In total, we are able to prove that 910 of the 969 nice holomorphic VOSAs with central charge 24 and with non-trivial odd part are strongly graded-local, without counting hypothetical fake copies of the shorter moonshine VOSA tensorized with a real free fermion VOSA. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24 Gaudio, Tiziano Quantum Algebra High Energy Physics - Theory Mathematical Physics Operator Algebras We prove that all nice holomorphic vertex operator superalgebras (VOSAs) with central charge at most 24 and with non-trivial odd part are unitary, apart from the hypothetical ones arising as fake copies of the shorter moonshine VOSA or of the latter tensorized with a real free fermion VOSA. Furthermore, excluding the ones with central charge 24 of glueing type III and with no real free fermion, we show that they are all strongly graded-local. In particular, they naturally give rise to holomorphic graded-local conformal nets. In total, we are able to prove that 910 of the 969 nice holomorphic VOSAs with central charge 24 and with non-trivial odd part are strongly graded-local, without counting hypothetical fake copies of the shorter moonshine VOSA tensorized with a real free fermion VOSA. |
| title | Unitarity and strong graded locality of holomorphic vertex operator superalgebras with central charge at most 24 |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2410.07099 |